WEBVTT

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OK.

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Uh, thank you all for attending
the Earthquake Science Seminar

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00:00:12.163 --> 00:00:13.289
weekly seminar series.

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00:00:13.299 --> 00:00:14.509
If you're new, welcome.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/304-0
00:00:14.799 --> 00:00:18.142
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00:00:18.142 --> 00:00:21.379
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00:00:21.379 --> 00:00:24.723
talks including this one will be
posted on the USGS earthquake

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science seminar web page.

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Close captioning can be turned
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page.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/359-0
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Rather, attendees during the
talk, please meet your mics and

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00:00:36.221 --> 00:00:37.419
turn off your cameras.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/425-0
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And so the Q&A session at
the end of the talk and feel

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/425-1
00:00:41.096 --> 00:00:45.011
free to submit your questions
via the chat at any time or wait

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/425-2
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to turn on your camera and ask
your question during the Q&A

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/425-3
00:00:48.988 --> 00:00:53.027
session after the talk specific
announcements for today, the All

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00:00:53.027 --> 00:00:55.699
Hands ESC meeting is tomorrow at
11:00 AM.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/443-0
00:00:55.909 --> 00:00:58.553
Please go to the link in your
teams calendar and look for the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/443-1
00:00:58.553 --> 00:00:58.809
email.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/455-0
00:01:00.679 --> 00:01:03.249
You're all welcome to join the
Gmag Science seminar.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/468-0
00:01:04.139 --> 00:01:07.809
Tomorrow, Thursday, July 27th at
10:30.

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00:01:08.659 --> 00:01:12.465
Elizabeth Barnes, a professor at
in atmospheric sciences at

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/505-1
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Colorado State University, will
be sharing her research titled

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/505-2
00:01:16.462 --> 00:01:20.459
AI for Climate Science, opening
the Black Box to Reveal Planet

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/505-3
00:01:20.459 --> 00:01:20.839
Earth.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/533-0
00:01:22.499 --> 00:01:26.028
USGS employees, if you have
special laboratory needs here at

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/533-1
00:01:26.028 --> 00:01:29.326
Moffett Field, please take a
look at the email from Andy

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/533-2
00:01:29.326 --> 00:01:29.789
Culvert.

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And finally, at the sign up
deadline for AGU is August 13th.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/576-0
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This year, CJ Meyers email for
the link and another reminder on

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that front.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/591-0
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The abstract internal submission
date is today, so keep that in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/591-1
00:01:43.411 --> 00:01:43.699
mind.

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And as always, the summer intern
meeting occurs weekly tomorrow,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/616-1
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Thursday at 1:00 PM, and they're
not ready for prime time.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/630-0
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Meeting occurs at 3:00 PM, so
please do tune into those with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/630-1
00:01:58.676 --> 00:01:59.169
that.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/638-0
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I will introduce today's
speaker.

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This is written by our very own
Catherine Materna, who is going

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/683-1
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to introduce Rishabh today, but
I was called away last minute

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for another obligation, so I'm
happy to read her introduction

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before we get into the talk.

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So we are very excited to have
Richard Malik give the seminar

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today.

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Rishav was a PhD student at the
Earth absorbing story in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/775-1
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Singapore, working on geodesy
and structural geology with Emma

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/775-2
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Hill and Judith Hubbard in his
PhD, he worked on a number of

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important problems such as block
modeling of deformation in the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/775-4
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Indo German region, where the
present day activity of the of

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the subduction zone is still
debated and the rise of the

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Shillong Plateau.

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Another effort in his PhD was
modeling a 32 year long slow

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/809-1
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slip event in Indonesia
constrained by Coral Records in

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the intertidal zone.

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Some of you, some of you may
have seen some of Reshop's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/853-1
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influential work on stress
constrained model, a coupling

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models of shallow subduction
zones, which was published in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/853-3
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Nature Geoscience as Lindsey at
all 2021.

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This work is helping us
understand that most parts of

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shallow megathrust like Cascadia
are probably coupled during the

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inner seismic period.

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A few years ago, Rishav then
moved to Caltech, where he's

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working with Mark Simons on
understanding the bulk Realogy,

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the crust and upper mantle, and
many other things.

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Something greater about rishav.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/946-0
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I love discussing new half baked
ideas with them because of his

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creativity and modeling.

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Know how it's a pleasure to have
Richard here today and we're

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excited for his talk.

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So Reshad with that?

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If you'd like to take us away on
your talk, we are excited to

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00:03:41.824 --> 00:03:42.079
hear.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/998-0
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Oh, thank you so much for having
me.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1007-0
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Umm, OK, let's see how this
works.

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00:03:49.669 --> 00:03:49.979
Yeah.

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OK.

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And my pointer is here can can
you see my pointer?

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Yes, we can.

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OK, great.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1044-0
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So thank you so much for having
me give this talk today.

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I'm gonna talk to you about the
earthquake cycle viscoelasticity

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and how it's important to
account for viscoelasticity

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while conducting numerical
simulations of plate boundary

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deformation.

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So this is especially important
as we try to relate short term

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observations like what we see
with seismograms and with

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00:04:25.979 --> 00:04:29.834
geodesy too much longer term
processes stored in the rock

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record.

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Umm, this figure here is from
one of my coauthors, Valerie

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Lambert at Santa Cruz.

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And it highlights the mechanical
coupling between frictional

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faults and the viscoelastic
bulk.

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So during the Intercisa Macally
locked period. The bulk

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accumulates viscous and elastic
strains and following an

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00:04:51.835 --> 00:04:54.639
earthquake on these frictional
faults.

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You can see there's an
accelerated release of this

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00:04:59.386 --> 00:05:01.609
stored energy good in the bulk.

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So if if anything, that's the
short summary of my talk that

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viscoelasticity matters.

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If if you go away with anything
like I guess that would be the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1255-1
00:05:12.835 --> 00:05:16.686
one sentence for it before we
get further ahead with this, I

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1255-2
00:05:16.686 --> 00:05:20.031
wanna make sure we're on the
same page about various

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1255-3
00:05:20.031 --> 00:05:22.429
constitutive relations and
realities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1269-0
00:05:23.539 --> 00:05:26.981
So I'm sure we all have some
intuition about linear

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1269-1
00:05:26.981 --> 00:05:27.709
elasticity.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1297-0
00:05:27.979 --> 00:05:31.129
It's where stress and strain are
proportional.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1305-0
00:05:31.979 --> 00:05:37.131
But Elasto plastic or elastic
frictional materials that those

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1305-1
00:05:37.131 --> 00:05:40.289
were, uh, it's elastic up to a
limit.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1316-0
00:05:40.379 --> 00:05:42.569
And then there's a yield stress
that's not exceeded.

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00:05:42.779 --> 00:05:46.069
So it's friction and some
plasticity formulations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1363-0
00:05:46.239 --> 00:05:49.620
It's a little more complicated
because the yield stress itself

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1363-1
00:05:49.620 --> 00:05:52.733
can vary as a function of sort
of the loading rate, time,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1363-2
00:05:52.733 --> 00:05:55.309
cumulative strain, and a bunch
of other things.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1392-0
00:05:55.399 --> 00:05:59.121
But the general idea is there's
an elastic domain, and then then

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1392-1
00:05:59.121 --> 00:06:01.239
you hit the sort of yield
condition.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1412-0
00:06:02.179 --> 00:06:06.324
A viscous body, on the other
hand, doesn't depend on strain,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1412-1
00:06:06.324 --> 00:06:10.129
but it has a relationship
between stress and the strain

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1412-2
00:06:10.129 --> 00:06:10.469
rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-0
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At least in steady state and so
Newtonian bodies are those which

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-1
00:06:15.256 --> 00:06:19.233
have a linear relationship
between stress and strain rate

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-2
00:06:19.233 --> 00:06:23.621
and power laws have a nonlinear
relationship and a viscoelastic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-3
00:06:23.621 --> 00:06:27.735
material is a material whose
stress depends on strain rate,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-4
00:06:27.735 --> 00:06:31.918
like a viscous material, but
also depends on strain, like an

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1477-5
00:06:31.918 --> 00:06:32.809
elastic body.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1509-0
00:06:33.329 --> 00:06:36.452
And so I'll go over the details
of this in a few slides, but

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1509-1
00:06:36.452 --> 00:06:39.729
that's the general idea of the
different constitutive relations

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1509-2
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that we'll discuss today.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1527-0
00:06:41.439 --> 00:06:44.499
And let's go up to the
earthquake cycle and see where

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1527-1
00:06:44.499 --> 00:06:45.859
viscoelasticity fits in.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1572-0
00:06:47.189 --> 00:06:51.968
So from the earthquake cycle
perspective, a strike slip

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1572-1
00:06:51.968 --> 00:06:57.004
boundary is just an A really
long fault whose shallow part

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1572-2
00:06:57.004 --> 00:07:00.844
ruptures in earthquakes
periodically or near

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1572-3
00:07:00.844 --> 00:07:05.879
periodically, and the deep part
creeps at a constant rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1591-0
00:07:06.029 --> 00:07:11.113
A seismically and this is maybe
the basis for most block motion

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1591-1
00:07:11.113 --> 00:07:13.099
models rigid body motion.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1619-0
00:07:13.579 --> 00:07:17.149
That's kind of this block like
motion enabled by slip on a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1619-1
00:07:17.149 --> 00:07:20.719
fault and these faults cut
through the entire lithosphere.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1639-0
00:07:21.639 --> 00:07:25.783
However, deformation in the
lower crust and upper mantle is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1639-1
00:07:25.783 --> 00:07:29.789
not fully localized, so this
picture is not exactly true.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1670-0
00:07:31.129 --> 00:07:36.926
So as we go to greater depths,
uh, what's this axis we, uh, the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1670-1
00:07:36.926 --> 00:07:42.179
temperature steadily increases
and frictional or brittle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1697-0
00:07:42.189 --> 00:07:46.498
Or these really localized
processes are replaced by more

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1697-1
00:07:46.498 --> 00:07:50.806
distributed or much broader uh
deformation which is much

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1697-2
00:07:50.806 --> 00:07:52.469
broader length scales.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1704-0
00:07:52.839 --> 00:07:54.999
And so we know this from looking
at.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1727-0
00:07:56.199 --> 00:08:00.107
Exhume share zones as well as
from lab derived theologies of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1727-1
00:08:00.107 --> 00:08:02.669
materials that make up the
lithosphere.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1753-0
00:08:03.159 --> 00:08:07.215
And there are maybe 2 main
reasons why I think about why I

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1753-1
00:08:07.215 --> 00:08:11.409
wanna model ductile deformation
during the earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1768-0
00:08:12.779 --> 00:08:15.809
One part of it is it's that's
it's fundamental science.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1790-0
00:08:15.819 --> 00:08:19.230
We want to know, we want to
understand how the lithosphere,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1790-1
00:08:19.230 --> 00:08:22.583
asthenosphere system works and
what the various mechanical

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1790-2
00:08:22.583 --> 00:08:23.379
couplings are.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1845-0
00:08:24.549 --> 00:08:28.829
But the other part is also to
some extent it's predictive

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1845-1
00:08:28.829 --> 00:08:33.109
because as we make the push to
develop more sophisticated

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1845-2
00:08:33.109 --> 00:08:37.906
earthquake sequence simulators,
we can't neglect the role of non

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1845-3
00:08:37.906 --> 00:08:42.702
elastic deformation of the bulk
in terms of the coupling of bulk

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1845-4
00:08:42.702 --> 00:08:46.539
deformation back with friction
on faults and so on.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1866-0
00:08:46.999 --> 00:08:50.388
So those are the two main
reasons that sort of motivate a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1866-1
00:08:50.388 --> 00:08:51.849
lot of this kind of work.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1876-0
00:08:52.779 --> 00:08:55.429
And so the layout of my talk is
as follows.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1893-0
00:08:55.679 --> 00:08:59.401
So first I'm gonna give you
details about how we model

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1893-1
00:08:59.401 --> 00:09:01.499
viscoelastic earthquake cycles.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1930-0
00:09:02.559 --> 00:09:06.347
I'll go over the governing PD
and and show you that we can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1930-1
00:09:06.347 --> 00:09:10.007
transform it into a set of
coupled ordinary differential

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1930-2
00:09:10.007 --> 00:09:13.859
equations and that lowers the
overall cost of running these

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1930-3
00:09:13.859 --> 00:09:14.629
simulations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1967-0
00:09:15.479 --> 00:09:19.201
And then I'll talk about some
important results and how we can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1967-1
00:09:19.201 --> 00:09:22.746
use this framework to estimate
geological properties of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1967-2
00:09:22.746 --> 00:09:26.055
lithosphere from geodetic
observations taken during the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1967-3
00:09:26.055 --> 00:09:27.059
earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/1977-0
00:09:27.309 --> 00:09:29.409
And I'll mainly focus on how
there are multiple.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2007-0
00:09:30.079 --> 00:09:33.652
Uh, there are multiple
viscoelastic formulations that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2007-1
00:09:33.652 --> 00:09:37.687
can explain geodetic data, and
I'm we're exploring what it's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2007-2
00:09:37.687 --> 00:09:40.929
gonna take to discriminate
between these various

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2007-3
00:09:40.929 --> 00:09:41.789
formulations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2030-0
00:09:42.289 --> 00:09:47.371
And I'll end with a slide or two
on transient theologies or non

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2030-1
00:09:47.371 --> 00:09:50.309
steady state viscoelastic
realities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2045-0
00:09:50.319 --> 00:09:53.327
And what they might mean for the
load bearing part of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2045-1
00:09:53.327 --> 00:09:53.949
lithosphere.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2056-0
00:09:54.859 --> 00:09:58.609
So to start with some details
about numerical simulations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2073-0
00:09:58.859 --> 00:10:04.358
So we're solving a quasi static
equilibrium equations in this

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2073-1
00:10:04.358 --> 00:10:04.979
medium.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2085-0
00:10:05.189 --> 00:10:10.529
So we split the domain into an
elasto frictional crust sitting.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2103-0
00:10:10.819 --> 00:10:15.983
Oops, sitting on a VISCO elastic
mantle, the top and bottom

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2103-1
00:10:15.983 --> 00:10:19.339
boundary conditions are traction
free.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2146-0
00:10:19.759 --> 00:10:25.709
Uh, the lateral edges are kept
at constant and opposite plate

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2146-1
00:10:25.709 --> 00:10:31.850
velocity, so this is simulating
far field plate like motion and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2146-2
00:10:31.850 --> 00:10:37.224
the various realities we we sort
of apply are so one is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2146-3
00:10:37.224 --> 00:10:38.279
elasticity.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2172-0
00:10:38.649 --> 00:10:44.913
So we're treating this entire
domain as elastic plus something

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2172-1
00:10:44.913 --> 00:10:51.178
so the entire domain is elastic,
except here it's elastic plus

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2172-2
00:10:51.178 --> 00:10:52.669
it's fictional.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2190-0
00:10:52.799 --> 00:10:56.125
So it's fictional on the fault,
and within this part it's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2190-1
00:10:56.125 --> 00:10:57.329
elastic plus viscous.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2211-0
00:10:57.339 --> 00:11:01.547
So it's viscoelastic and there
are a few different ways to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2211-1
00:11:01.547 --> 00:11:04.899
parameterize uh, these non
elastic theologies.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2236-0
00:11:05.309 --> 00:11:09.024
You could have the elastic and
the nonelastic parts in series

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2236-1
00:11:09.024 --> 00:11:12.500
like you have for a Maxwell
body, or in laster frictional

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2236-2
00:11:12.500 --> 00:11:12.859
Brody.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2279-0
00:11:14.739 --> 00:11:19.785
So in these springs dashboard or
spring slider systems, uh, it's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2279-1
00:11:19.785 --> 00:11:24.521
the same stress that is shared
across both elements, but the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2279-2
00:11:24.521 --> 00:11:28.169
strain is a sum of the two
individual strains.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2310-0
00:11:28.639 --> 00:11:32.100
And then you can also have this
third type of material, which is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2310-1
00:11:32.100 --> 00:11:35.348
a Burger's body, so it has an
elastic material that has this

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2310-2
00:11:35.348 --> 00:11:36.999
permanent deformation and then.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2371-0
00:11:37.709 --> 00:11:42.156
Uh, this is an elastic element
which gives you it gives you

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2371-1
00:11:42.156 --> 00:11:46.752
recoverable deformation, but
there's a delay in time and this

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2371-2
00:11:46.752 --> 00:11:51.273
sort of material brings in a
transient or a non steady state

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2371-3
00:11:51.273 --> 00:11:55.720
Realogy because the relationship
between stress and viscous

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2371-4
00:11:55.720 --> 00:12:00.389
strains is not unique due to the
delay in this element anyway.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2408-0
00:12:00.459 --> 00:12:03.626
So this is the mechanical
problem we want to solve, but

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2408-1
00:12:03.626 --> 00:12:07.133
the idea is we don't want to
really solve the full PD because

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2408-2
00:12:07.133 --> 00:12:10.187
then we'd have to mesh
everything and be very careful

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2408-3
00:12:10.187 --> 00:12:10.979
about meshing.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2414-0
00:12:11.579 --> 00:12:12.079
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2433-0
00:12:12.609 --> 00:12:16.127
Instead, what we wanna do is use
some techniques to reduce the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2433-1
00:12:16.127 --> 00:12:17.299
computational burden.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2460-0
00:12:17.729 --> 00:12:20.868
And to gain some insight into
how we do this, I'm gonna start

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2460-1
00:12:20.868 --> 00:12:23.955
with a much simpler system and
then build up complexity from

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2460-2
00:12:23.955 --> 00:12:24.259
there.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2479-0
00:12:24.269 --> 00:12:27.054
So we'll start with the spring
slider and then move to a 2D

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2479-1
00:12:27.054 --> 00:12:28.029
viscoelastic problem.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2492-0
00:12:29.249 --> 00:12:32.639
So here's a spring slider in
series.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2521-0
00:12:33.089 --> 00:12:37.487
It's being driven at constant
velocity, and so both of these

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2521-1
00:12:37.487 --> 00:12:41.597
elements experience the same
stress, while the strain is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2521-2
00:12:41.597 --> 00:12:43.399
additive between the two.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2562-0
00:12:44.429 --> 00:12:48.629
Umm so so the stress in the
system for the elastic part is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2562-1
00:12:48.629 --> 00:12:52.901
just the sheer modulus times
whatever is the strain the the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2562-2
00:12:52.901 --> 00:12:57.101
purely elastic strain that this
spring experiences and the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2562-3
00:12:57.101 --> 00:12:57.599
slider.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2566-0
00:12:58.209 --> 00:12:59.919
Uh, yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2586-0
00:12:59.929 --> 00:13:02.654
Here we are basically saying
it's the friction coefficient

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2586-1
00:13:02.654 --> 00:13:04.639
which is given by rate and state
friction.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2595-0
00:13:04.649 --> 00:13:06.099
But you can use whatever
friction you want.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2637-0
00:13:07.469 --> 00:13:12.963
UM and the equilibrium condition
is then just the time derivative

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2637-1
00:13:12.963 --> 00:13:18.208
of this stress, and so we get
the time derivative of stress is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2637-2
00:13:18.208 --> 00:13:23.452
basically the spring constant
times some the stored the stored

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2637-3
00:13:23.452 --> 00:13:26.449
strings within the elastic
element.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2700-0
00:13:27.099 --> 00:13:31.374
OK, so this is an ode and we can
numerically integrate this

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2700-1
00:13:31.374 --> 00:13:35.862
through time and so we'll have
our full solution, but this has

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2700-2
00:13:35.862 --> 00:13:39.923
no spatial dimensions to the
problem to bring in spatial

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2700-3
00:13:39.923 --> 00:13:44.483
dimensions into this problem, we
need to now compute an elastic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2700-4
00:13:44.483 --> 00:13:46.549
interaction kernel capital K.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2725-0
00:13:47.369 --> 00:13:51.105
So in the spring slider case,
this case was just a small, just

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2725-1
00:13:51.105 --> 00:13:54.484
a number, but in the finite
dimensional case this is the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2725-2
00:13:54.484 --> 00:13:54.899
matrix.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2756-0
00:13:54.909 --> 00:13:59.268
It's a full interaction kernel
and it's actually solutions of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2756-1
00:13:59.268 --> 00:14:03.486
the same equilibrium equations,
but for an elastic material

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2756-2
00:14:03.486 --> 00:14:06.649
subject to the relevant boundary
conditions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2792-0
00:14:07.939 --> 00:14:12.802
So the resulting OD now for this
one default in a 2D medium, it's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2792-1
00:14:12.802 --> 00:14:16.559
it looks the same as it did for
the spring slider.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2827-0
00:14:16.659 --> 00:14:21.555
It's it's, except it's a higher
dimensional thing and we can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2827-1
00:14:21.555 --> 00:14:26.612
expand from 1D1D meshes to 2D
mesh because we also have greens

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2827-2
00:14:26.612 --> 00:14:28.859
functions for displacements.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2857-0
00:14:28.869 --> 00:14:32.744
These are greens functions for
displacements and stresses for

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2857-1
00:14:32.744 --> 00:14:36.307
both localized slip on faults as
well As for distributed

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2857-2
00:14:36.307 --> 00:14:37.869
deformation and a volume.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2893-0
00:14:38.579 --> 00:14:42.227
This is the work of Silvan
Barbeau and colleagues, and so

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2893-1
00:14:42.227 --> 00:14:46.251
this allows us to construct the
full interaction kernel into DD

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2893-2
00:14:46.251 --> 00:14:50.339
for bulk deformation, and these
are analytical greens functions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2925-0
00:14:52.159 --> 00:14:56.801
The last thing that is left for
us to compute is, uh, the the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2925-1
00:14:56.801 --> 00:15:00.993
loading rate and the loading
rate for the spring slider

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2925-2
00:15:00.993 --> 00:15:03.239
problem and for the UH1D mesh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2938-0
00:15:03.349 --> 00:15:05.959
Was it was just a uniform, but a
single number.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2957-0
00:15:06.409 --> 00:15:10.394
But for a viscoelastic problem
there is a spatial dependence to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2957-1
00:15:10.394 --> 00:15:11.079
it, and so.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2980-0
00:15:11.399 --> 00:15:16.162
But that's kind of easy to deal
with because all we do is we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2980-1
00:15:16.162 --> 00:15:19.909
just solve the same divergences
of stress is 0.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/2993-0
00:15:19.919 --> 00:15:22.009
But now we just do it for the
viscous problem.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3020-0
00:15:22.179 --> 00:15:25.432
So we have sort of split up the
problem into a viscous problem

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3020-1
00:15:25.432 --> 00:15:28.529
and elastic problem and then we
can sum back the solutions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3023-0
00:15:29.359 --> 00:15:29.899
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3039-0
00:15:30.259 --> 00:15:34.049
And so there's a very nice
analytical solution for this.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3051-0
00:15:34.089 --> 00:15:37.424
There's calculated by more in
Parsons for arbitrary

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3051-1
00:15:37.424 --> 00:15:38.129
theologies.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3068-0
00:15:38.599 --> 00:15:42.947
So now we know the long term
loading rate and the long term

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3068-1
00:15:42.947 --> 00:15:43.889
loading rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3082-0
00:15:44.189 --> 00:15:49.079
Uh, sort of depends on the on
the formulation that you use.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3093-0
00:15:49.369 --> 00:15:50.799
So it depends on this end.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3106-0
00:15:50.809 --> 00:15:53.896
So for power laws versus for
Newtonian cases, solutions will

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3106-1
00:15:53.896 --> 00:15:55.009
be slightly different.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3136-0
00:15:55.849 --> 00:16:00.713
Here I'm showing you the the
long term velocities in the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3136-1
00:16:00.713 --> 00:16:05.918
viscous domain for a Newtonian
fluid and this is for a power

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3136-2
00:16:05.918 --> 00:16:06.259
law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3171-0
00:16:06.269 --> 00:16:11.398
When N is 3 and you can see
there's a lot more localization

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3171-1
00:16:11.398 --> 00:16:16.954
as N gets higher and so you can
think of the the sort of the far

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3171-2
00:16:16.954 --> 00:16:20.629
extent of this is the asymptotic
limit of.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3182-0
00:16:20.639 --> 00:16:23.479
It is as N gets really really
large.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3203-0
00:16:23.849 --> 00:16:27.560
You basically collapse all of
this onto a fictional system and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3203-1
00:16:27.560 --> 00:16:30.799
so forth is Infinity would just
get you back friction.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3227-0
00:16:31.229 --> 00:16:34.892
So OK, so now we know how to
compute the long term velocities

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3227-1
00:16:34.892 --> 00:16:37.019
and strain rates within the
domain.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3241-0
00:16:37.529 --> 00:16:41.019
So we have a system of coupled
odds that we need to integrate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3280-0
00:16:41.089 --> 00:16:44.658
So that's this set of equations
and if we wanted to study how

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3280-1
00:16:44.658 --> 00:16:47.824
earthquake nucleation and
rupture worked, we were just

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3280-2
00:16:47.824 --> 00:16:51.221
impose velocity, weakening
frictional conditions somewhere

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3280-3
00:16:51.221 --> 00:16:52.199
within the fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3300-0
00:16:52.769 --> 00:16:55.530
Uh, choose some initial
conditions and let the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3300-1
00:16:55.530 --> 00:16:58.409
simulation run and wait for the
results instead.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-0
00:16:58.419 --> 00:17:01.558
Today I'm discussing
applications for inverse

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-1
00:17:01.558 --> 00:17:05.516
problems, so we don't really
want to solve for the actual

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-2
00:17:05.516 --> 00:17:09.815
earthquake, but we wanna impose
it and then see how the system

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-3
00:17:09.815 --> 00:17:13.636
evolves to that imposed
coseismic stress change the way

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-4
00:17:13.636 --> 00:17:17.662
we do that is we are imposing
cost slip, so the earthquake

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-5
00:17:17.662 --> 00:17:22.166
slip is imposed and that results
in a stress change everywhere in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-6
00:17:22.166 --> 00:17:26.533
the medium and that gives us the
relevant initial conditions to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3385-7
00:17:26.533 --> 00:17:28.239
drive our system of odds.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3410-0
00:17:29.039 --> 00:17:33.076
Umm, the thing to remember with
these kinds of simulations is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3410-1
00:17:33.076 --> 00:17:36.528
specially for nonlinear
theologies to get mechanical

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3410-2
00:17:36.528 --> 00:17:37.309
consistency.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3420-0
00:17:37.859 --> 00:17:40.169
Uh, you need to spin up the
simulations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3438-0
00:17:40.179 --> 00:17:45.589
So what spin up means is we need
to repeat the cycle of loading.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3449-0
00:17:45.799 --> 00:17:49.039
Evaluate Lord Lord with an
earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3463-0
00:17:49.049 --> 00:17:52.327
Evaluate a number of times until
we reach cycle invariant

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3463-1
00:17:52.327 --> 00:17:52.779
results.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3521-0
00:17:53.109 --> 00:17:57.488
So here is an example of this
where I'm showing you stress

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3521-1
00:17:57.488 --> 00:18:01.644
evolving with time at a few
different points within the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3521-2
00:18:01.644 --> 00:18:06.320
medium, as shown in Eric Catlins
paper from quite a while ago,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3521-3
00:18:06.320 --> 00:18:10.699
you can see that each of these
wiggles is 1 cycle and each

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3521-4
00:18:10.699 --> 00:18:14.039
color is different points within
the domain.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3535-0
00:18:14.049 --> 00:18:17.789
So it takes a while before you
get cycle invariant results.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3542-0
00:18:19.509 --> 00:18:21.789
OK, so now that's the method.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3551-0
00:18:22.929 --> 00:18:24.229
They'll establish how it works.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3565-0
00:18:24.999 --> 00:18:28.593
I want to talk about the, uh,
interesting stuff, which is some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3565-1
00:18:28.593 --> 00:18:29.049
results.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3584-0
00:18:29.059 --> 00:18:33.365
And So what I'll talk about now
is, UM, straight about strain

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3584-1
00:18:33.365 --> 00:18:36.629
rate localization during the
earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3608-0
00:18:37.179 --> 00:18:41.242
I'll also talk about the
coupling of viscous creep with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3608-1
00:18:41.242 --> 00:18:45.449
after slip and some implications
for stress transfer now.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3624-0
00:18:45.459 --> 00:18:48.048
After that, I'll move on to
discussing comparison with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3624-1
00:18:48.048 --> 00:18:50.119
geodetic observations and
inverse problems.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3628-0
00:18:51.579 --> 00:18:51.929
OK.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3654-0
00:18:52.419 --> 00:18:56.922
So to Orient you with what I'm
showing you is I'm only showing

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3654-1
00:18:56.922 --> 00:19:00.209
you the the view of the viscous
strain rates.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3670-0
00:19:00.519 --> 00:19:04.076
This is the permanent
deformation rate within the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3670-1
00:19:04.076 --> 00:19:07.349
viscoelastic domain at three
different times.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3679-0
00:19:08.489 --> 00:19:11.559
Umm, so this is immediately
after the earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3711-0
00:19:11.569 --> 00:19:14.473
This is some time after the
earthquake and this is at the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3711-1
00:19:14.473 --> 00:19:17.777
very end of the earthquake cycle
so late in the Intersect period,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3711-2
00:19:17.777 --> 00:19:19.379
just before the next earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3739-0
00:19:20.499 --> 00:19:23.983
So if we look at a linear
Maxwell Realogy, so N is 1 uh,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3739-1
00:19:23.983 --> 00:19:27.589
that's an elastic spring in
series within Newtonian fluid.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3745-0
00:19:29.569 --> 00:19:30.469
This is what it looks like.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3761-0
00:19:30.479 --> 00:19:33.595
This is strained rates at
different times and we compare

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3761-1
00:19:33.595 --> 00:19:34.579
it to a power law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3784-0
00:19:35.009 --> 00:19:39.088
Because NS-3 and you can see
there's just a lot more

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3784-1
00:19:39.088 --> 00:19:41.859
localization with these power
laws.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3814-0
00:19:42.169 --> 00:19:45.576
In fact, most of the
viscoelastic medium is basically

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3814-1
00:19:45.576 --> 00:19:49.676
behaving purely elastically for
these parallels, so it's like we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3814-2
00:19:49.676 --> 00:19:52.199
have a down dip extension of the
fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3868-0
00:19:52.309 --> 00:19:56.830
It's just a bit broader, but it
never really diffuses outwards

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3868-1
00:19:56.830 --> 00:20:00.777
like it does for the linear
Maxwell case with Burger's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3868-2
00:20:00.777 --> 00:20:04.724
bodies, though, the initial
response is a lot like the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3868-3
00:20:04.724 --> 00:20:09.389
linear Maxwell, but late in the
Intersect period, strain rate is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3868-4
00:20:09.389 --> 00:20:10.609
not as diffusive.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3910-0
00:20:10.719 --> 00:20:15.227
It appears to have localized
quite a bit, and so the burgers

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3910-1
00:20:15.227 --> 00:20:18.921
body sort of like this
approximate it's somewhere

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3910-2
00:20:18.921 --> 00:20:23.281
between what the the linear
theology is predicted and what

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3911-0
00:20:22.269 --> 00:20:24.999
The but nevertheless.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3910-3
00:20:23.281 --> 00:20:24.389
the power laws.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3915-0
00:20:27.409 --> 00:20:29.099
Alright, alright.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3936-0
00:20:29.109 --> 00:20:32.079
And the second topic I wanna I
wanna highlight.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3939-0
00:20:29.219 --> 00:20:32.009
Alright, that's something that I
wanna I wanna.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3942-0
00:20:33.039 --> 00:20:34.369
So I'm getting a lot of
feedback.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3951-0
00:20:36.089 --> 00:20:38.419
OK, it's gone alright.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3971-0
00:20:38.529 --> 00:20:41.473
So the second topic I wanna
highlight is the coupling

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3971-1
00:20:41.473 --> 00:20:44.199
between viscous creep and
frictional after sleep.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3996-0
00:20:44.549 --> 00:20:48.939
So in this figure I'm showing
you basically 3 lines and the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/3996-1
00:20:48.939 --> 00:20:53.109
three lines are at three
different points in the medium.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4014-0
00:20:53.119 --> 00:20:57.759
The Black line is uh for a
frictional part in the domain,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4014-1
00:20:57.759 --> 00:20:59.759
so that's somewhere here.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4044-0
00:20:59.989 --> 00:21:05.209
This blue line is out there and
the brown line is there and I'm

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4044-1
00:21:05.209 --> 00:21:09.939
showing you some normalized
velocity or strain rate as it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4044-2
00:21:09.939 --> 00:21:13.609
evolves in time during the
earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4062-0
00:21:14.929 --> 00:21:20.424
So the blue and orange lines
show you a sort of very standard

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4062-1
00:21:20.424 --> 00:21:22.019
exponential decay.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4076-0
00:21:22.529 --> 00:21:25.863
Uh, which is what you would
expect for a linear Maxwell

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4076-1
00:21:25.863 --> 00:21:26.399
material.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4109-0
00:21:26.969 --> 00:21:30.670
But if you look at the black
line, which is, you know, in the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4109-1
00:21:30.670 --> 00:21:34.490
fictional domain, the frictional
evolution is supposed to, it's

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4109-2
00:21:34.490 --> 00:21:36.639
supposed to evolve
logarithmically.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4119-0
00:21:36.929 --> 00:21:38.469
So it should have been a
straight line.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4153-0
00:21:38.999 --> 00:21:43.937
Umm, but instead it sort of
starts off that way and then it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4153-1
00:21:43.937 --> 00:21:49.122
starts to follow what the what
the bulk is sort of imposing on

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4153-2
00:21:49.122 --> 00:21:49.369
it.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4167-0
00:21:49.379 --> 00:21:52.774
It starts to mimic what's
happening in the viscous the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4167-1
00:21:52.774 --> 00:21:54.009
viscoelastic domain.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4191-0
00:21:54.459 --> 00:21:59.067
So this indicates that the
mechanical coupling, at least

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4191-1
00:21:59.067 --> 00:22:03.755
within you know reasonable
parameter regimes is for large

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4191-2
00:22:03.755 --> 00:22:05.129
earthquakes also.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4237-0
00:22:06.729 --> 00:22:12.279
It's a lot stronger from the
viscous mantle to the down depth

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4237-1
00:22:12.279 --> 00:22:18.098
limit of frictional sliding, and
so yeah, this is partly because

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4237-2
00:22:18.098 --> 00:22:23.917
there's just more material that
can deform viscously than it can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4237-3
00:22:23.917 --> 00:22:25.349
uh frictionally.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4243-0
00:22:25.729 --> 00:22:28.129
So that's one way of thinking
about it and.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4262-0
00:22:29.029 --> 00:22:32.719
Umm, if you are looking to
simplify after slip models.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4311-0
00:22:33.209 --> 00:22:37.104
Uh, instead of evaluating the
full interactions you you can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4311-1
00:22:37.104 --> 00:22:41.194
just consider sort of one way
time dependent loading from this

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4311-2
00:22:41.194 --> 00:22:45.413
script to driving after slip in
addition to whatever the initial

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4311-3
00:22:45.413 --> 00:22:48.269
conditions and the background
slip rate is.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4339-0
00:22:49.419 --> 00:22:54.131
But I thought that was kind of
an interesting result that we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4339-1
00:22:54.131 --> 00:22:57.839
found that after slip is uh, it
doesn't really.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4363-0
00:22:58.229 --> 00:23:01.564
There's no decoupling between
after slip and viscous script,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4363-1
00:23:01.564 --> 00:23:04.570
but there is a it's it's
slightly simpler problem than

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4363-2
00:23:04.570 --> 00:23:06.429
evaluating the full
interactions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4392-0
00:23:08.099 --> 00:23:10.909
OK, the last topic I want to
mention before we switch gears

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4392-1
00:23:10.909 --> 00:23:13.953
and talk about data fitting and
inverse problems is the topic of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4392-2
00:23:13.953 --> 00:23:14.609
stress change.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4432-0
00:23:15.219 --> 00:23:19.959
So here I'm showing you the
stress component needed to drive

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4432-1
00:23:19.959 --> 00:23:24.310
slip on a vertical fault at 10
kilometers depth and the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4432-2
00:23:24.310 --> 00:23:29.282
horizontal axis is time and so
the different colors are a bunch

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4432-3
00:23:29.282 --> 00:23:30.059
of things.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4504-0
00:23:30.069 --> 00:23:35.412
So the Gray line is the stress
change as it evolves in time for

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4504-1
00:23:35.412 --> 00:23:40.421
a purely Elasto frictional
simulation, and the yellow, blue

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4504-2
00:23:40.421 --> 00:23:45.763
and the sum total which is red
is for a viscoelastic medium, so

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4504-3
00:23:45.763 --> 00:23:50.856
it's a frictional fault in a
viscoelastic medium and you can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4504-4
00:23:50.856 --> 00:23:54.779
see that stress transfer due to
viscous creep.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4513-0
00:23:56.259 --> 00:23:59.283
The OR the coupling between
viscous creep and frictional

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4513-1
00:23:59.283 --> 00:24:00.609
after slip is a lot more.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4566-0
00:24:00.799 --> 00:24:05.761
It's just a much larger
amplitude when you evaluate it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4566-1
00:24:05.761 --> 00:24:11.264
on the fault, then a purely
frictional uh and purely elastic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4566-2
00:24:11.264 --> 00:24:15.774
bulk and even the stress
transfer just due to the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4566-3
00:24:15.774 --> 00:24:21.458
frictional part itself is much
larger than in a purely elastic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4566-4
00:24:21.458 --> 00:24:22.089
medium.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4596-0
00:24:22.099 --> 00:24:25.794
And this is because viscous
creep then drives deep after

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4596-1
00:24:25.794 --> 00:24:29.748
slip, and so after slip ends up
loading the salesman generic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4596-2
00:24:29.748 --> 00:24:30.979
parts of the fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4606-0
00:24:30.989 --> 00:24:34.439
More and this is not just on the
fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4636-0
00:24:34.809 --> 00:24:39.727
Even as you go farther away, so
10 or 20 kilometers away from

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4636-1
00:24:39.727 --> 00:24:44.327
the fault, you end up with
significantly different stress

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4636-2
00:24:44.327 --> 00:24:47.579
levels as stress transfer into
the bulk.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4663-0
00:24:47.759 --> 00:24:51.460
And so this is something that we
might want to consider as we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4663-1
00:24:51.460 --> 00:24:54.743
move into more realistic
simulations of regional fault

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4663-2
00:24:54.743 --> 00:24:55.519
interactions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4703-0
00:24:57.489 --> 00:25:02.007
OK, that's the same important
results and in the next part of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4703-1
00:25:02.007 --> 00:25:06.234
the talk, I want to discuss some
qualitative and slightly

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4703-2
00:25:06.234 --> 00:25:10.753
quantitative comparisons of the
results of the simulations we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4703-3
00:25:10.753 --> 00:25:13.959
ran with the earthquake cycle
observations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4740-0
00:25:14.389 --> 00:25:18.199
The goal is to use uh
observations like late intersex

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4740-1
00:25:18.199 --> 00:25:22.855
strain rate localization and the
spatial temporal pattern of post

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4740-2
00:25:22.855 --> 00:25:27.087
seismic relaxation to calibrate
our real logical models and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4740-3
00:25:27.087 --> 00:25:28.639
associated parameters.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4786-0
00:25:29.049 --> 00:25:33.263
The thing you need to stress on
is we don't know for certain

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4786-1
00:25:33.263 --> 00:25:37.201
what is the true or what's the
actual formulation of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4786-2
00:25:37.201 --> 00:25:41.277
constitutive relation for
viscoelasticity at, you know, at

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4786-3
00:25:41.277 --> 00:25:44.109
depths greater than, say, 20
kilometers.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4791-0
00:25:44.119 --> 00:25:45.389
Is it a power law?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4799-0
00:25:45.519 --> 00:25:46.859
Is it a burger's body?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4813-0
00:25:48.839 --> 00:25:51.709
We don't really know, or at
least I don't know.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4836-0
00:25:52.239 --> 00:25:56.252
The goal is to develop the tools
and inform how we run

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4836-1
00:25:56.252 --> 00:26:00.119
experiments that allow us to
answer these questions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4848-0
00:26:01.159 --> 00:26:02.679
So that's what we're gonna see
in the next few slides.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4854-0
00:26:03.759 --> 00:26:05.069
Umm, OK.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4869-0
00:26:05.189 --> 00:26:09.669
So the way we work this works is
we have a geodetic time series.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4889-0
00:26:09.939 --> 00:26:13.148
So this is the time series of
displacements at sites near the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4889-1
00:26:13.148 --> 00:26:14.959
fault and far away from the
fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4913-0
00:26:16.769 --> 00:26:20.762
The box and the right is post
seismic displacements for a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4913-1
00:26:20.762 --> 00:26:24.479
given site, and all of these
lines are snap velocity.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4925-0
00:26:24.489 --> 00:26:26.839
Snapshots at different times
during the earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4966-0
00:26:28.329 --> 00:26:32.389
So to understand what typical
post seismic observations are,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4966-1
00:26:32.389 --> 00:26:36.715
we can fit an exponential decay
to this to get a relaxation time

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4966-2
00:26:36.715 --> 00:26:40.376
scale and the exponential
function is expected for any

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4966-3
00:26:40.376 --> 00:26:42.439
damped linear dynamical system.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4975-0
00:26:42.499 --> 00:26:43.989
So that's the motivation for
that choice.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4998-0
00:26:44.859 --> 00:26:48.701
Umm, the other observation we
care about is what happens late

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/4998-1
00:26:48.701 --> 00:26:52.109
in the inter seismic period when
everything is steady.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5029-0
00:26:52.579 --> 00:26:57.999
So we expect the spatial pattern
to have this S like shape and we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5029-1
00:26:57.999 --> 00:27:02.679
can fit an arc tangent to it and
derive a locking depth.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5059-0
00:27:03.639 --> 00:27:07.837
And in the other part of this
late intersect period is the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5059-1
00:27:07.837 --> 00:27:12.248
time series at any given point
should be a straight line with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5059-2
00:27:12.248 --> 00:27:13.529
minimal curvature.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5093-0
00:27:13.539 --> 00:27:18.981
So that means this S shape
should be stationary in time, so

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5093-1
00:27:18.981 --> 00:27:24.514
this is just real observations
from umm, mature strike, slip

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5093-2
00:27:24.514 --> 00:27:29.049
faults, continental strike, slip
faults globally.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5105-0
00:27:29.479 --> 00:27:31.919
You can see that this S shaped
feature is real.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5123-0
00:27:32.659 --> 00:27:37.599
Umm, this is from a compilation
by uh vernant in 2015.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5145-0
00:27:37.609 --> 00:27:41.761
It's been some of the slip rates
have been updated ever since,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5145-1
00:27:41.761 --> 00:27:44.529
but the pattern is more or less
the same.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5147-0
00:27:45.519 --> 00:27:46.149
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5172-0
00:27:46.859 --> 00:27:51.260
And the locking depth is about
10 to 20 kilometers, which is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5172-1
00:27:51.260 --> 00:27:53.569
consistent with the seismogenic.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5174-0
00:27:53.659 --> 00:27:54.769
So that's this.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5195-0
00:27:54.879 --> 00:27:59.838
It's it's consistent with the
seismogenic depth that we expect

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5195-1
00:27:59.838 --> 00:28:01.569
for continental crust.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5210-0
00:28:01.939 --> 00:28:09.179
So the post seismic period has a
very funny signal that you see.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5220-0
00:28:09.259 --> 00:28:13.409
So in time you see this elevated
creep rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5241-0
00:28:13.659 --> 00:28:17.238
So this is displacement and this
is time, so it's much faster at

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5241-1
00:28:17.238 --> 00:28:18.889
the start and it's slows down.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5243-0
00:28:19.339 --> 00:28:20.009
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5269-0
00:28:20.439 --> 00:28:23.477
And so a lot of studies take
this early part of the time

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5269-1
00:28:23.477 --> 00:28:26.249
series and fit an exponential
decay function to it.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5312-0
00:28:26.499 --> 00:28:31.631
The time scale that they get out
there is about a year or so, and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5312-1
00:28:31.631 --> 00:28:35.519
when you extend the
observational window to a lot

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5312-2
00:28:35.519 --> 00:28:40.107
longer, you end up getting time
scales, which also sort of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5312-3
00:28:40.107 --> 00:28:42.129
increases the window size.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-0
00:28:42.619 --> 00:28:45.994
So one viable explanation for
this is this is a power law

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-1
00:28:45.994 --> 00:28:49.428
Realogy because power law is
exhibit this full spectrum of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-2
00:28:49.428 --> 00:28:52.803
relaxation time scales, and this
particular example for a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-3
00:28:52.803 --> 00:28:55.713
following, the Hector mine
earthquake in Southern

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-4
00:28:55.713 --> 00:28:59.262
California is part of the most
motivation for what I'm gonna

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5375-5
00:28:59.262 --> 00:29:01.939
show you and some of the inverse
methodology.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5421-0
00:29:02.219 --> 00:29:06.367
Because the same observations
can be explained by a parlor

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5421-1
00:29:06.367 --> 00:29:10.515
Realogy, as the authors did in
the previous case or with a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5421-2
00:29:10.515 --> 00:29:15.014
linear Burger's body, as these
authors do, and many others have

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5421-3
00:29:15.014 --> 00:29:16.279
done this as well.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5438-0
00:29:17.409 --> 00:29:23.993
So as long as you can create
these sort of two effective

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5438-1
00:29:23.993 --> 00:29:25.379
viscosities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5459-0
00:29:25.389 --> 00:29:30.362
So one viscosity which is early
on, which is quite low and that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5459-1
00:29:30.362 --> 00:29:33.859
evolves to a much higher
viscosity later on.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5474-0
00:29:34.129 --> 00:29:38.279
So if you can do that, the
observations don't seem to care.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5486-0
00:29:39.109 --> 00:29:42.019
Umm, what is the actual
formulation?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5530-0
00:29:42.829 --> 00:29:46.611
The data is fit relatively
identically, and so then the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5530-1
00:29:46.611 --> 00:29:50.259
question we were asking
ourselves is what exactly can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5530-2
00:29:50.259 --> 00:29:53.771
observations really inform us,
or like what kind of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5530-3
00:29:53.771 --> 00:29:58.026
observations we need to tell the
difference between this these

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5530-4
00:29:58.026 --> 00:29:59.039
two theologies?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5566-0
00:30:00.349 --> 00:30:05.027
So one thing that are simulation
results did tell us is maybe we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5566-1
00:30:05.027 --> 00:30:09.705
can forget about uh homogeneous
linear Maxwell type of realities

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5566-2
00:30:09.705 --> 00:30:13.879
to explain observations from the
entire earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5593-0
00:30:14.089 --> 00:30:20.059
So what we have here is on the Y
axis is inter seismic locking

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5593-1
00:30:20.059 --> 00:30:24.039
depth and on the X axis is the
viscosity.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5618-0
00:30:24.049 --> 00:30:27.698
For linear viscoelastic
material, or sort of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5618-1
00:30:27.698 --> 00:30:32.539
prefactor for power laws and the
different colored lines are for

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5618-2
00:30:32.539 --> 00:30:34.699
N increasing from one to six.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5630-0
00:30:36.339 --> 00:30:39.489
Umm, here we impose an
earthquake every 50 years.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5676-0
00:30:39.579 --> 00:30:43.543
So 50 years of strain build up
and then release and the Gray

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5676-1
00:30:43.543 --> 00:30:47.181
region is what we consider as
acceptable locking depths

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5676-2
00:30:47.181 --> 00:30:51.080
because in our simulation the
elastic the seismogenic layer

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5676-3
00:30:51.080 --> 00:30:53.289
thickness is about 20
kilometers.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5697-0
00:30:53.299 --> 00:30:56.653
So we are allowing about you
know 100% error, so 20 to 40

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5697-1
00:30:56.653 --> 00:30:57.289
kilometers.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5719-0
00:30:59.079 --> 00:31:02.589
You're very generous that way
for the linear case.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5723-0
00:31:02.979 --> 00:31:08.385
Viscosity is out here can
explain the early possess mic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5723-1
00:31:08.385 --> 00:31:10.219
relaxation pattern.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5762-0
00:31:11.229 --> 00:31:14.983
While these cities are like 10
to the 20 or so basically have

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5762-1
00:31:14.983 --> 00:31:18.616
no measurable perturbation to
the earthquake cycle, so they

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5762-2
00:31:18.616 --> 00:31:22.431
don't really show any curvature
or any relaxation pattern, but

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5762-3
00:31:22.431 --> 00:31:25.579
the locking depths are the other
way around, right?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5785-0
00:31:25.589 --> 00:31:28.879
Like out here you have late
intercement locking depths are

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5785-1
00:31:28.879 --> 00:31:31.109
really huge, like 100 kilometers
or so.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5838-0
00:31:31.389 --> 00:31:35.594
And whereas on this end of this
you have pretty reasonable

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5838-1
00:31:35.594 --> 00:31:39.656
locking depths, so and when you
increase the size of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5838-2
00:31:39.656 --> 00:31:44.289
earthquake, so now there's four
times larger, the latent seismic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5838-3
00:31:44.289 --> 00:31:48.423
locking depths for these low
viscosity uh simulations are

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5838-4
00:31:48.423 --> 00:31:49.919
even more ridiculous.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5844-0
00:31:49.929 --> 00:31:51.389
It's like really unrealistic.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5890-0
00:31:52.009 --> 00:31:55.710
So in contrast, if you look at
sort of these lines out here,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5890-1
00:31:55.710 --> 00:31:59.290
these are for the power laws,
the these show locking debts

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5890-2
00:31:59.290 --> 00:32:03.233
that are more or less consistent
with the seismogenic thickness,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5890-3
00:32:03.233 --> 00:32:05.599
they aren't really changing very
much.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5907-0
00:32:06.629 --> 00:32:09.641
And if you look at linear
burgers realities, there are a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5907-1
00:32:09.641 --> 00:32:11.279
lot like the power law results.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5925-0
00:32:11.719 --> 00:32:15.994
So each of these lines, the
thicker line is for a really

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5925-1
00:32:15.994 --> 00:32:17.269
large earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-0
00:32:17.279 --> 00:32:21.502
So every 200 years, while this
really thin line is for an

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-1
00:32:21.502 --> 00:32:26.234
earthquake that occurs every 50
years and they all have the same

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-2
00:32:26.234 --> 00:32:30.529
short term viscosity and the
horizontal axis is giving you

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-3
00:32:30.529 --> 00:32:35.188
the long term viscosity and it's
mainly the long term viscosity

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-4
00:32:35.188 --> 00:32:39.774
that controls the late intersec
locking depth and they can all

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/5997-5
00:32:39.774 --> 00:32:42.759
fit the early relaxation part
just fine.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6008-0
00:32:43.489 --> 00:32:46.675
And there are also consistent
with latent seismic locking

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6008-1
00:32:46.675 --> 00:32:47.059
depths.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6025-0
00:32:47.169 --> 00:32:52.259
So seems like linear Maxwell
realities can't do the job.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6036-0
00:32:52.269 --> 00:32:55.419
But burgers and power laws work.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6051-0
00:32:56.209 --> 00:33:01.150
The other part of about you know
of rejecting realities was we

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6051-1
00:33:01.150 --> 00:33:01.699
expect.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6057-0
00:33:02.349 --> 00:33:03.939
So this is a time series.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6075-0
00:33:04.289 --> 00:33:08.069
We expect that the late
intercement locking depth to be

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6075-1
00:33:08.069 --> 00:33:09.959
more or less steady in time.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6084-0
00:33:11.309 --> 00:33:13.639
Uh, with the linear Maxwell type
Realogy?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6090-0
00:33:13.649 --> 00:33:16.009
Sort of starts seeing this.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6092-0
00:33:16.109 --> 00:33:16.639
Uh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6132-0
00:33:16.679 --> 00:33:21.564
Ever increasing trend of as you
go on as you go in time the the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6132-1
00:33:21.564 --> 00:33:25.228
locking depth just keeps
increasing and the the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6132-2
00:33:25.228 --> 00:33:29.350
wavelength of uh strain
accumulation just gets larger

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6132-3
00:33:29.350 --> 00:33:30.189
and larger.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6149-0
00:33:30.739 --> 00:33:33.206
And so that's not really
consistent with what we're

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6149-1
00:33:33.206 --> 00:33:34.439
seeing in the data so far.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6185-0
00:33:34.839 --> 00:33:37.880
So, OK, we have eliminated
linear Maxwell from our pool of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6185-1
00:33:37.880 --> 00:33:40.922
realistic realities, but it
seems we can't really tell the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6185-2
00:33:40.922 --> 00:33:43.499
difference between linear
burgers and power loss.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6211-0
00:33:44.829 --> 00:33:48.212
So to find out what it'll take
to tell the difference between

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6211-1
00:33:48.212 --> 00:33:51.049
those two realities, we came up
with an experiment.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6247-0
00:33:51.119 --> 00:33:56.142
So it's the same 2D strike slip
plate boundary as before, except

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6247-1
00:33:56.142 --> 00:34:00.856
now we're imposing this depth
dependent flow parameters from

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6247-2
00:34:00.856 --> 00:34:02.479
hearth and kohlstedt.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6279-0
00:34:03.499 --> 00:34:07.659
These include both diffusion
creep and dislocation creep, so

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6279-1
00:34:07.659 --> 00:34:11.477
the viscous component has
basically a linear term and a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6279-2
00:34:11.477 --> 00:34:14.409
nonlinear term, and their depth
dependent.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6289-0
00:34:14.419 --> 00:34:17.859
So this is to simulate uh,
little closer to what?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6308-0
00:34:18.079 --> 00:34:22.248
You know the earth might be, and
we're subjecting this to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6308-1
00:34:22.248 --> 00:34:24.189
periodic earthquake cycles.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6332-0
00:34:24.579 --> 00:34:27.915
And then we use about 20 years
of data to do the inverse

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6332-1
00:34:27.915 --> 00:34:30.139
problem and then the inverse
problem.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-0
00:34:30.599 --> 00:34:33.613
We're trying to infer a
spatially uniform set of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-1
00:34:33.613 --> 00:34:37.610
parameters for the power law as
well As for linear burgers body,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-2
00:34:37.610 --> 00:34:41.546
and then we're gonna compare the
residuals and for the periodic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-3
00:34:41.546 --> 00:34:45.482
cycles we are one of the things
that we are varying is the size

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-4
00:34:45.482 --> 00:34:49.172
of the earthquake and that we
vary by basically varying the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6401-5
00:34:49.172 --> 00:34:50.709
repeat time of the event.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6413-0
00:34:50.719 --> 00:34:54.319
So 50 or events are smaller and
200 year events are larger.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6457-0
00:34:55.379 --> 00:35:00.399
We also run earthquake sequences
where we chose to a we choose a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6457-1
00:35:00.399 --> 00:35:05.264
total moment, and then we varied
how it's partitioned into two

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6457-2
00:35:05.264 --> 00:35:09.589
events, both in magnitude and
the time in between them.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6500-0
00:35:09.719 --> 00:35:14.028
And we are again estimating the
best fit parameters for each

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6500-1
00:35:14.028 --> 00:35:18.196
real logical model class and
then we want to see for those

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6500-2
00:35:18.196 --> 00:35:22.505
best fit parameters are the
residuals you know significantly

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6500-3
00:35:22.505 --> 00:35:25.119
improved by any single class or
not.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6525-0
00:35:26.279 --> 00:35:30.097
OK, for the periodic cycles,
they basically get the same

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6525-1
00:35:30.097 --> 00:35:34.249
result as I showed you for the
Hector mine case, the misfits.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6533-0
00:35:34.339 --> 00:35:35.569
So just the misfits.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6562-0
00:35:35.819 --> 00:35:38.943
And these are each of the
different simulations of small

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6562-1
00:35:38.943 --> 00:35:42.506
earthquake, big earthquake, very
big earthquake, the misfits for

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6562-2
00:35:42.506 --> 00:35:44.369
linear burgers and parlor
models.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6578-0
00:35:44.719 --> 00:35:47.628
They're not sufficiently
different, and so you can't

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6578-1
00:35:47.628 --> 00:35:49.219
convincingly tell them apart.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6587-0
00:35:50.449 --> 00:35:52.459
There's a little bit of
difference.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6613-0
00:35:52.569 --> 00:35:57.207
Uh, based on if we include
constraints from the inter

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6613-1
00:35:57.207 --> 00:36:02.017
seismic period or not with the
workers bodies, but that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6613-2
00:36:02.017 --> 00:36:04.679
difference is relatively small.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6621-0
00:36:04.769 --> 00:36:06.709
It's consistent, but it's still
quite small.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6652-0
00:36:08.499 --> 00:36:12.423
What I'm plotting down here is
the results of the periodic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6652-1
00:36:12.423 --> 00:36:16.614
cycles for every 200 years for
this batch, only the black line

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6652-2
00:36:16.614 --> 00:36:18.609
is the synthetic observations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6664-0
00:36:20.469 --> 00:36:23.809
We actually work with the full
time series here.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6672-0
00:36:23.819 --> 00:36:25.579
I'm just for the sake of
plotting.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6737-0
00:36:25.829 --> 00:36:29.464
I'm showing you the first
principal component, so this is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6737-1
00:36:29.464 --> 00:36:33.286
a spatial part of the PC and
this is the first time function

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6737-2
00:36:33.286 --> 00:36:37.046
for the principal component and
it turns out that the first

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6737-3
00:36:37.046 --> 00:36:41.057
principal component has almost
90% of the variance, so you know

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6737-4
00:36:41.057 --> 00:36:44.629
it's it's a fair representation
of the full time series.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6764-0
00:36:45.899 --> 00:36:49.048
The green box is the near field,
so it's close to the fault and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6764-1
00:36:49.048 --> 00:36:51.902
we don't really use it in the
inversion because we're not

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6764-2
00:36:51.902 --> 00:36:53.969
trying to estimate frictional
properties.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6770-0
00:36:53.979 --> 00:36:56.709
We want really the bulk
viscoelastic properties.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6780-0
00:36:58.439 --> 00:37:00.919
I'll note that the fit is not
perfect.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6815-0
00:37:01.679 --> 00:37:06.719
You can see that in the time and
space, because the underlying

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6815-1
00:37:06.719 --> 00:37:11.439
the true model was, it was depth
dependent and it had some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6815-2
00:37:11.439 --> 00:37:14.719
complicated power, law and
linear terms.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6829-0
00:37:15.409 --> 00:37:18.800
And we are fitting it with
basically just a spatially

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6829-1
00:37:18.800 --> 00:37:20.369
uniform parameterization.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6833-0
00:37:21.159 --> 00:37:21.619
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6845-0
00:37:21.989 --> 00:37:26.015
Also, we don't really have this
friction plus viscous stuff

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6845-1
00:37:26.015 --> 00:37:26.619
going on.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6864-0
00:37:26.629 --> 00:37:31.033
We just have viscous, so we're
not able to account for any of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6864-1
00:37:31.033 --> 00:37:33.519
the frictional contributions,
but.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6900-0
00:37:35.129 --> 00:37:38.621
That said, among our models
among our inverse models,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6900-1
00:37:38.621 --> 00:37:42.566
there's very it's very hard to
tell the difference between a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6900-2
00:37:42.566 --> 00:37:44.959
linear burgers type and a power
law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6911-0
00:37:47.049 --> 00:37:50.826
But with earthquake sequences,
I'm the results are quite

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6911-1
00:37:50.826 --> 00:37:51.489
different.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6932-0
00:37:51.499 --> 00:37:55.634
We can tell linear burgers and
power laws apart in large part

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6932-1
00:37:55.634 --> 00:37:58.369
of the parameter space that we
explored.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6953-0
00:37:58.379 --> 00:38:03.476
So what we did is we basically
chose a total seismic moment

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6953-1
00:38:03.476 --> 00:38:05.429
cumulate over 2 events.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6962-0
00:38:05.479 --> 00:38:09.079
So that would be the equivalent
of uh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/6968-0
00:38:09.089 --> 00:38:10.779
Periodic event every 200 years.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7005-0
00:38:10.789 --> 00:38:15.598
We just divided up them up in
time, and so the horizontal axis

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7005-1
00:38:15.598 --> 00:38:20.559
is the time span between the two
events and the vertical axis is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7005-2
00:38:20.559 --> 00:38:23.459
the relative ratio of the two
events.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7044-0
00:38:23.589 --> 00:38:27.411
So for example, here .1 is the
first event is small, and the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7044-1
00:38:27.411 --> 00:38:31.107
next event is really big,
whereas out here the first event

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7044-2
00:38:31.107 --> 00:38:34.239
was really big and the next
event is quite small.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7057-0
00:38:35.579 --> 00:38:38.249
OK, so you varied the timing and
relative magnitudes.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7074-0
00:38:38.819 --> 00:38:43.159
The colors here show you the
relative improvement for a power

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7074-1
00:38:43.159 --> 00:38:45.889
law model compared to a burgers
model.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7111-0
00:38:46.259 --> 00:38:52.171
So for most of these results,
you can see, uh, it's like if if

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7111-1
00:38:52.171 --> 00:38:57.896
the events were a year apart or
so or about .3 or more units

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7111-2
00:38:57.896 --> 00:38:59.679
apart in magnitude.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7136-0
00:39:00.469 --> 00:39:04.742
Umm, you got 50% up to 50%
difference in the Misfits,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7136-1
00:39:04.742 --> 00:39:09.489
that's 50% improvement in the
Misfits by a power law model.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7157-0
00:39:09.939 --> 00:39:13.917
So the reason is because the
underlying synthetic simulations

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7157-1
00:39:13.917 --> 00:39:15.329
were from a power law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7195-0
00:39:15.639 --> 00:39:19.480
And when you perturb a power law
system with different size

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7195-1
00:39:19.480 --> 00:39:23.576
earthquakes, the relaxation time
scale and the amplitude is not

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7195-2
00:39:23.576 --> 00:39:27.417
really a constant, unlike what
you would have with a linear

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7195-3
00:39:27.417 --> 00:39:28.569
burgers type body.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7212-0
00:39:28.719 --> 00:39:31.779
This is why the two theological
models they sort of diverge.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7227-0
00:39:32.059 --> 00:39:34.334
The two classes diverge and
that's why you can tell the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7227-1
00:39:34.334 --> 00:39:35.309
difference between them.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7247-0
00:39:36.709 --> 00:39:42.350
However, even with the power law
model, UM, the parameters that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7247-1
00:39:42.350 --> 00:39:44.729
we estimate are non unique.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7265-0
00:39:44.899 --> 00:39:48.971
So you can see this in the
exponent and the prefactor that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7265-1
00:39:48.971 --> 00:39:49.799
we estimate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7294-0
00:39:52.089 --> 00:39:58.687
There the the color is the the
residual misfits residual and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7294-1
00:39:58.687 --> 00:40:04.636
you can see that they don't
really pull out any unique

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7294-2
00:40:04.636 --> 00:40:05.609
solution.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7309-0
00:40:05.919 --> 00:40:10.039
Uh, the trade off perfectly and
the resulting time series.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7322-0
00:40:10.959 --> 00:40:15.307
Also, we've just drawn a bunch
of samples from within that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7322-1
00:40:15.307 --> 00:40:15.749
range.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-0
00:40:16.059 --> 00:40:20.111
They all seem to evolve almost
identically, so I'm not

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-1
00:40:20.111 --> 00:40:24.532
convinced that geodesy alone can
use to figure out what the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-2
00:40:24.532 --> 00:40:29.395
effective logical parameters are
for the lithosphere, you need to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-3
00:40:29.395 --> 00:40:33.962
think of some clever ways in
which we can combine lab derived

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-4
00:40:33.962 --> 00:40:38.088
flow laws with geodetic
observations and possibly other

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7384-5
00:40:38.088 --> 00:40:39.709
kinds of observations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7392-0
00:40:39.819 --> 00:40:42.509
For example, something that I've
come across recently.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7419-0
00:40:42.929 --> 00:40:46.038
Uh, I don't really understand
how to use it, but I've just

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7419-1
00:40:46.038 --> 00:40:49.095
come across and it's quite
exciting is uh with Sharif and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7419-2
00:40:49.095 --> 00:40:49.569
isotropy.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7422-0
00:40:50.199 --> 00:40:50.509
Uh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7442-0
00:40:51.199 --> 00:40:55.152
If if anyone knows how how it
works and how it can be used,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7442-1
00:40:55.152 --> 00:40:56.469
uh, that'd be great.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7449-0
00:40:56.479 --> 00:40:58.409
I have the next slide. I have.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7467-0
00:40:58.419 --> 00:41:02.405
Uh, a slightly older paper,
which I'm sort of using to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7467-1
00:41:02.405 --> 00:41:04.869
motivate how it could be
helpful.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7477-0
00:41:07.189 --> 00:41:09.759
So this is a paper from 2003.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7514-0
00:41:09.989 --> 00:41:14.793
Uh, that seemed to solve this
problem by using by sort of by

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7514-1
00:41:14.793 --> 00:41:19.912
estimating the anisotropy along
the Dead Sea transform fault and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7514-2
00:41:19.912 --> 00:41:21.959
what they found was there.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7564-0
00:41:21.969 --> 00:41:27.058
Is this the nearly 30 kilometer
wide shares on at lower crustal

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7564-1
00:41:27.058 --> 00:41:31.033
or upper mantle depths that
polarized share waves

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7564-2
00:41:31.033 --> 00:41:35.088
differently than the
surroundings did and this can

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7564-3
00:41:35.088 --> 00:41:39.699
place sort of bound on how high
end can be for flow loss.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7577-0
00:41:39.709 --> 00:41:45.128
So these different figures are
the extent of localization for

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7577-1
00:41:45.128 --> 00:41:46.439
different ends.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7582-0
00:41:46.729 --> 00:41:47.959
Uh end values?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7617-0
00:41:48.329 --> 00:41:52.894
Uh, so this is for N is 1 and
it's two and it's 3 N is 6 here

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7617-1
00:41:52.894 --> 00:41:57.017
and you can see that it gets
progressively narrower and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7617-2
00:41:57.017 --> 00:41:57.679
narrower.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-0
00:41:58.009 --> 00:42:03.173
And so with the with the
ambiguity that we had, we we the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-1
00:42:03.173 --> 00:42:08.782
ambiguity that we had in sort of
UM recovering the the logical

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-2
00:42:08.782 --> 00:42:14.480
parameters, we saw that the we
couldn't really constrain and it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-3
00:42:14.480 --> 00:42:19.822
was like covarying with the
prefactor like across basically

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-4
00:42:19.822 --> 00:42:25.163
all possible values of north
greater than two or so and but

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-5
00:42:25.163 --> 00:42:30.861
but The thing is as N increases
you start getting more and more

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7696-6
00:42:30.861 --> 00:42:32.909
localized shares zones.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7758-0
00:42:33.239 --> 00:42:37.639
And so if you have a way to
estimate that, no, the shares

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7758-1
00:42:37.639 --> 00:42:42.569
and has to be at least about 30
kilometers wide or 40 kilometers

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7758-2
00:42:42.569 --> 00:42:47.120
wide, that sets a bound on how
large N can be and that will

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7758-3
00:42:47.120 --> 00:42:51.899
allow us to sort of narrow the
domain of reasonable solutions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7763-0
00:42:51.909 --> 00:42:53.239
And it's an independent
constraint.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7770-0
00:42:54.149 --> 00:42:55.539
So that's just an idea.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7814-0
00:42:55.899 --> 00:43:00.162
I'm happy to talk about this
with anyone who can help me out

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7814-1
00:43:00.162 --> 00:43:04.424
with this, so on a slightly
different topic, I also wanna go

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7814-2
00:43:04.424 --> 00:43:08.546
back to the late intersect
period for power law theologies

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7814-3
00:43:08.546 --> 00:43:12.599
and sort of talk a little more
about transient realities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7841-0
00:43:13.399 --> 00:43:16.911
Umm, so I wonder where the last
few slides trying to tell the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7841-1
00:43:16.911 --> 00:43:20.366
difference between a power law
theology and a linear burgers

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7841-2
00:43:20.366 --> 00:43:20.649
body?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7876-0
00:43:21.259 --> 00:43:25.144
There's something interesting
about the latent racism period

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7876-1
00:43:25.144 --> 00:43:28.710
for power law theology that
perhaps suggests we need to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7876-2
00:43:28.710 --> 00:43:32.085
update how we parameterize
viscous realities for the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7876-3
00:43:32.085 --> 00:43:32.849
lithosphere.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7917-0
00:43:33.699 --> 00:43:38.404
Umm So what happens in the late
intersec period is that the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7917-1
00:43:38.404 --> 00:43:42.873
strain rate localizes and
reaches a sort of quasi steady

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7917-2
00:43:42.873 --> 00:43:47.969
state, similar to what you would
expect for a stress free crack.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7957-0
00:43:48.179 --> 00:43:52.042
So if you replace this entire
bulk deformation by the sit down

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7957-1
00:43:52.042 --> 00:43:55.844
deep extension of the fault held
the bottom of the fault at a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7957-2
00:43:55.844 --> 00:43:58.849
constant velocity, and the top
of it was pinned.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7968-0
00:43:59.199 --> 00:44:00.939
You would get the stress free
crack solution.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7991-0
00:44:02.469 --> 00:44:07.875
Now if we move this bottom
traction from brown dry slightly

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/7991-1
00:44:07.875 --> 00:44:11.929
lower, the shape of this would
be preserved.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8002-0
00:44:11.979 --> 00:44:14.289
Shape of the solution is
preserved, but it just gets

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8002-1
00:44:14.289 --> 00:44:14.899
stretched now.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8018-0
00:44:16.789 --> 00:44:19.976
So this would result in what
would appear to be a deeper

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8018-1
00:44:19.976 --> 00:44:20.759
locking depth.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8035-0
00:44:21.189 --> 00:44:24.719
So what I mean by that is you're
looking at surface velocities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8048-0
00:44:25.269 --> 00:44:29.282
The blue lines are for
simulations where the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8048-1
00:44:29.282 --> 00:44:30.709
lithosphere, uh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8060-0
00:44:31.299 --> 00:44:35.079
The thickness is about 40
kilometers and the pink lines.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8074-0
00:44:36.509 --> 00:44:40.059
Here are for little sphere
thickness of 100 kilometers.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8084-0
00:44:40.869 --> 00:44:44.439
The fault is always fixed to be
20 kilometers thick.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8141-0
00:44:44.549 --> 00:44:48.331
It's just the viscous
viscoelastic domain thickness

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8141-1
00:44:48.331 --> 00:44:52.840
that we are playing with and
this is the resulting uh surface

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8141-2
00:44:52.840 --> 00:44:57.204
velocity field and this is the
estimated locking depth from

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8141-3
00:44:57.204 --> 00:45:01.495
trying to fit this S shaped
curve and you can see that the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8141-4
00:45:01.495 --> 00:45:05.059
domain depth and the locking
depth they sort of.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8143-0
00:45:05.449 --> 00:45:06.409
They covary.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8145-0
00:45:06.999 --> 00:45:07.579
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8173-0
00:45:08.359 --> 00:45:12.801
And So what this means is that
there is in our parallel

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8173-1
00:45:12.801 --> 00:45:16.609
realities there is this domain
size dependence.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8207-0
00:45:16.669 --> 00:45:20.325
And so if you need domain size
independent latent seismic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8207-1
00:45:20.325 --> 00:45:23.980
strain rates, we would need
Realogy that stiffens up more

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8207-2
00:45:23.980 --> 00:45:26.879
than expected from steady state
viscous laws.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8227-0
00:45:27.479 --> 00:45:31.844
UM, and so that would be like a
transient realogy, something

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8227-1
00:45:31.844 --> 00:45:32.989
like uh sourced.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8230-0
00:45:32.999 --> 00:45:34.039
The transient is of course.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8233-0
00:45:35.619 --> 00:45:35.919
I think.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8264-0
00:45:36.219 --> 00:45:39.798
We can talk about that later,
but however you get that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8264-1
00:45:39.798 --> 00:45:43.702
transient, so it has to just
stiffen up more than you would

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8264-2
00:45:43.702 --> 00:45:45.979
expect from just the steady
state.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8268-0
00:45:46.269 --> 00:45:48.389
Uh from yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8305-0
00:45:48.399 --> 00:45:53.826
From a steady state flow law,
umm, there's another explanation

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8305-1
00:45:53.826 --> 00:45:58.994
for this, which is UM, just
could be that the middle or the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8305-2
00:45:58.994 --> 00:46:02.009
lower crust is anomalously
strong.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8362-0
00:46:02.079 --> 00:46:06.242
It's so strong that it's simply
doesn't participate in the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8362-1
00:46:06.242 --> 00:46:10.616
earthquake cycle, and so during
the late intersect period, it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8362-2
00:46:10.616 --> 00:46:15.201
prevents this stress free crack
behavior and it sort of it shows

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8362-3
00:46:15.201 --> 00:46:18.799
locking depths that are
controlled entirely by the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8362-4
00:46:18.799 --> 00:46:20.069
seismogenic depth.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8381-0
00:46:20.139 --> 00:46:24.691
And it sort of decouples the
seismogenic thickness from the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8381-1
00:46:24.691 --> 00:46:27.649
deeper part of the of the
lithosphere.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8410-0
00:46:27.659 --> 00:46:32.310
So the upper mantle and the
upper cruster sort of decoupled

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8410-1
00:46:32.310 --> 00:46:36.884
during the earthquake cycle by
this very high load bearing

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8410-2
00:46:36.884 --> 00:46:37.349
layer.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8416-0
00:46:37.729 --> 00:46:39.769
Uh, that's another possibility.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8445-0
00:46:41.289 --> 00:46:46.358
So either a transit theology or
this extreme heterogeneity is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8445-1
00:46:46.358 --> 00:46:51.263
something that could explain
domain size independent latent

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8445-2
00:46:51.263 --> 00:46:53.389
or size mixed train rates.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8478-0
00:46:54.649 --> 00:46:59.283
And with that, I'm gonna wrap
things up and just tell you that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8478-1
00:46:59.283 --> 00:47:03.844
we started by talking about how
do we model earthquake cycles

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8478-2
00:47:03.844 --> 00:47:06.639
and we needed three main
ingredients.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8485-0
00:47:06.949 --> 00:47:09.919
We needed an elastic interaction
kernel.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8489-0
00:47:10.089 --> 00:47:10.629
Ask.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8520-0
00:47:11.159 --> 00:47:14.404
We needed some closed form
expressions for how we load the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8520-1
00:47:14.404 --> 00:47:17.979
system, so that's the stressing
rate and then we needed the long

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8520-2
00:47:17.979 --> 00:47:19.189
term deformation rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8530-0
00:47:19.199 --> 00:47:23.089
So with these three we can do
VISCO elastic earthquake cycles.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8561-0
00:47:25.259 --> 00:47:29.270
I also told you and tried to
convince you that linear burgers

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8561-1
00:47:29.270 --> 00:47:33.217
and parla realities can match
geodetic observations from the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8561-2
00:47:33.217 --> 00:47:34.769
entire earthquake cycle.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8596-0
00:47:34.779 --> 00:47:39.963
So that's post seismic and inter
seismic umm for periodic events,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8596-1
00:47:39.963 --> 00:47:44.833
but the the predictions from
these models start to diverge as

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8596-2
00:47:44.833 --> 00:47:47.739
you go towards earthquake
sequences.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8616-0
00:47:47.749 --> 00:47:52.368
So when the events are of
different size and they're not

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8616-1
00:47:52.368 --> 00:47:55.609
really recurring, they're not
periodic.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8633-0
00:47:55.619 --> 00:47:59.389
So there is the footprint of one
event in the other and so on.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8663-0
00:47:59.919 --> 00:48:03.208
You can start to tell them
apart, but even if you could

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8663-1
00:48:03.208 --> 00:48:06.908
tell them apart and you could
say that, uh, the maybe the true

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8663-2
00:48:06.908 --> 00:48:08.259
reality is a power law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8689-0
00:48:09.579 --> 00:48:13.798
You're not solved the problem
because power law parameters are

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8689-1
00:48:13.798 --> 00:48:17.816
highly non unique and we need
some other ways to, you know,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8689-2
00:48:17.816 --> 00:48:19.289
break this degeneracy.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8695-0
00:48:20.429 --> 00:48:21.959
Umm, yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-0
00:48:21.969 --> 00:48:26.542
So that's my last point, that
the inverse problem has some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-1
00:48:26.542 --> 00:48:31.426
mixed determined parameters, so
there's some parameter that is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-2
00:48:31.426 --> 00:48:35.146
actually a really well
constrained, because the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-3
00:48:35.146 --> 00:48:39.565
combination of these two is
really well constrained, but

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-4
00:48:39.565 --> 00:48:44.370
individually they're not, and
the last point that I mentioned

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-5
00:48:44.370 --> 00:48:49.176
is there seems to be a need for
either a really heterogeneous

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8764-6
00:48:49.176 --> 00:48:51.889
strength profile by
heterogeneous.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8777-0
00:48:51.899 --> 00:48:57.069
I don't mean, uh, like varying a
lot over short length scales.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8823-0
00:48:57.079 --> 00:49:01.173
It just mean the middle crust
has to be really strong compared

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8823-1
00:49:01.173 --> 00:49:04.681
to what you would expect from
just doing post seismic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8823-2
00:49:04.681 --> 00:49:08.580
relaxation studies or maybe it
is a transient sort of a non

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8823-3
00:49:08.580 --> 00:49:10.529
steady state kind of theology.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8842-0
00:49:11.059 --> 00:49:14.434
And with that, I'm happy to take
any questions and chat about

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8842-1
00:49:14.434 --> 00:49:16.339
whatever you think is
interesting.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8848-0
00:49:24.219 --> 00:49:25.029
Thanks, Roshan.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8867-0
00:49:25.419 --> 00:49:31.437
With that, let's open it up for
questions and see that and Fred

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8867-1
00:49:31.437 --> 00:49:33.129
Paul the question.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8881-0
00:49:33.139 --> 00:49:34.919
Fred, do you wanna meet yourself
and ask your question?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8882-0
00:49:36.619 --> 00:49:37.049
Yes.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8892-0
00:49:37.279 --> 00:49:40.479
Thanks Rachel for super
interesting talk.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8902-0
00:49:40.529 --> 00:49:43.429
Uh, you're taking on a really
complicated problem.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8938-0
00:49:43.499 --> 00:49:47.551
There's not only the time scales
of the bulk viscoelastic

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8938-1
00:49:47.551 --> 00:49:52.022
relaxation, but also after slip
which interferes with this kind

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8938-2
00:49:52.022 --> 00:49:53.699
of analysis in practice.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8964-0
00:49:54.719 --> 00:49:59.673
Umm yeah, I was wondering if
possibly with real earthquake

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8964-1
00:49:59.673 --> 00:50:04.458
you could try to distinguish
between the burgers and the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8964-2
00:50:04.458 --> 00:50:05.969
nonlinear Realogy.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8979-0
00:50:05.979 --> 00:50:09.865
I'm thinking of perhaps no the
Ridgecrest earthquake which

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/8979-1
00:50:09.865 --> 00:50:11.709
hasn't the sequence, hasn't.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9000-0
00:50:11.859 --> 00:50:15.707
It hasn't gone on for very long
since it happened, but also the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9000-1
00:50:15.707 --> 00:50:16.789
Denali earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9005-0
00:50:16.539 --> 00:50:16.659
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9056-0
00:50:16.899 --> 00:50:21.244
It's been quite a long time
since that happened, and I know

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9056-1
00:50:21.244 --> 00:50:25.806
a number of reality models were
proposed soon after the Denali

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9056-2
00:50:25.806 --> 00:50:30.078
earthquake, and then Jeff
Frymoyer had an AGU presentation

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9056-3
00:50:30.078 --> 00:50:34.423
where he compared them with a
longer amount of observations

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9056-4
00:50:34.423 --> 00:50:37.899
and found that nobody's models
were doing well.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9052-0
00:50:34.939 --> 00:50:35.189
Right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9076-0
00:50:38.389 --> 00:50:42.892
And so maybe hidden in that data
set, you might be able to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9076-1
00:50:42.892 --> 00:50:45.029
distinguish between the two.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9085-0
00:50:45.699 --> 00:50:48.769
Right, so I I I think I think
you're right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9104-0
00:50:48.779 --> 00:50:54.326
Like for the right experiment
there is, there is a way to

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9104-1
00:50:54.326 --> 00:50:58.629
maybe tell the difference,
especially in 3D?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9110-0
00:50:58.939 --> 00:51:00.249
Not so much in 2D.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9129-0
00:51:02.479 --> 00:51:07.509
To the, especially for 2D uh
anti plane strain there is.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9154-0
00:51:07.519 --> 00:51:10.918
I don't think there is any way
to tell the difference, because

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9154-1
00:51:10.918 --> 00:51:13.669
there's just one component of
displacements in 3D.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9180-0
00:51:13.819 --> 00:51:18.128
The vertical seem to be quite
instructive on like what is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9180-1
00:51:18.128 --> 00:51:22.511
going on, or at least it's
instructive on what the process

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9180-2
00:51:22.511 --> 00:51:23.699
length scale is.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-0
00:51:25.659 --> 00:51:30.170
I'm I I wanna point out one of
the things that you know, maybe

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-1
00:51:30.170 --> 00:51:34.393
I didn't talk about which is
this idea of like the initial

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-2
00:51:34.393 --> 00:51:37.973
conditions that you need
especially for power law

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-3
00:51:37.973 --> 00:51:42.412
theologies parlor Realogy is a
super sensitive to that choice

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-4
00:51:42.412 --> 00:51:46.851
of pre earthquake strain rates
and the the spatial scale over

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9253-5
00:51:46.851 --> 00:51:49.929
which you impose this prereqs
strain rate.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9274-0
00:51:49.939 --> 00:51:54.662
So you could get a power law
rheology to basically fit

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9274-1
00:51:54.662 --> 00:51:56.809
anything that you wanted.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9320-0
00:51:56.919 --> 00:52:00.342
If you impose the right, if you,
if you kept the pre earthquake

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9320-1
00:52:00.342 --> 00:52:03.817
strain rate as a free parameter
that I think some people have in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9320-2
00:52:03.817 --> 00:52:07.293
the past and so we tried to get
around that by, you know, trying

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9320-3
00:52:07.293 --> 00:52:08.309
and spinning it up.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9354-0
00:52:08.539 --> 00:52:12.262
But by spinning up and
earthquake cycle you also have

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9354-1
00:52:12.262 --> 00:52:16.813
this problem of you need to know
that that is that is a Long live

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9354-2
00:52:16.813 --> 00:52:17.709
mature fault.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9372-0
00:52:18.529 --> 00:52:22.977
And so, like, that's some long
lived mature fault with the well

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9372-1
00:52:22.977 --> 00:52:25.339
defined share zone underneath
it.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9402-0
00:52:25.409 --> 00:52:29.956
So for places like Denali, I
don't know if you could really

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9402-1
00:52:29.956 --> 00:52:34.579
tell the difference between a
linear burgers or a power law.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9408-0
00:52:34.589 --> 00:52:36.009
Or maybe they both just.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9432-0
00:52:37.189 --> 00:52:41.702
They're both insufficient models
for the Denali case before

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9432-1
00:52:41.702 --> 00:52:45.689
Hector mine and Landers, and
maybe so far with rich.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9472-0
00:52:45.699 --> 00:52:49.240
I haven't seen a lot of posts,
seismic studies with Rich Crest

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9472-1
00:52:49.240 --> 00:52:52.556
yet, but for Hector mine and
Lander, is it it isn't really

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9472-2
00:52:52.556 --> 00:52:55.984
very clear that you can even
tell the difference between the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9472-3
00:52:55.984 --> 00:52:56.209
two.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9486-0
00:52:56.219 --> 00:53:00.149
There, the overall misfits are
almost identical, especially

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9486-1
00:53:00.149 --> 00:53:02.899
because people remove the pre
earthquake.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9504-0
00:53:04.239 --> 00:53:09.972
Velocities from the post
earthquake time series, UMM, and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9504-1
00:53:09.972 --> 00:53:11.949
and so there's this.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9565-0
00:53:12.099 --> 00:53:15.121
There's this correction that's
happening beforehand, so all

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9565-1
00:53:15.121 --> 00:53:18.194
your fitting is a curved line
which flattens out at the end,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9565-2
00:53:18.194 --> 00:53:21.115
and then you can put in any
number that you want as a pre

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9565-3
00:53:21.115 --> 00:53:24.389
earthquake strain rate and then
you will you will be able to fit

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9565-4
00:53:24.389 --> 00:53:27.159
it with the power law or with
the linear burgers body.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9584-0
00:53:27.169 --> 00:53:31.089
So answer is I I I can't.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9575-0
00:53:29.449 --> 00:53:30.039
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9586-0
00:53:30.629 --> 00:53:31.699
Yeah, it's a tall order.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9597-0
00:53:31.099 --> 00:53:32.159
I yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9598-0
00:53:31.769 --> 00:53:34.229
Yeah, to do with the real
situation.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9617-0
00:53:34.279 --> 00:53:36.679
Yeah, it's worth trying anyway.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9616-0
00:53:35.649 --> 00:53:35.929
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9635-0
00:53:36.329 --> 00:53:41.714
I I I think with insar umm it's
it's slightly more possible than

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9635-1
00:53:41.714 --> 00:53:44.199
it was only with farfield GPS.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-0
00:53:44.909 --> 00:53:49.094
Simply because if there is a
migratory segment, so if there

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-1
00:53:49.094 --> 00:53:53.558
is a non stationary signal, if
the dominant length the dominant

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-2
00:53:53.558 --> 00:53:57.813
depth at which deformation is
occurring is changing in time,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-3
00:53:57.813 --> 00:54:01.998
then that wavelength of the
deformation will also change on

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-4
00:54:01.998 --> 00:54:05.973
the surface and that is
something that we would see with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9702-5
00:54:05.973 --> 00:54:09.949
insar but not so much if you
only had farfield stations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9707-0
00:54:11.709 --> 00:54:13.139
So possibly.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9728-0
00:54:13.149 --> 00:54:16.828
But I mean, we have to do the
experiment to to answer your

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9723-0
00:54:16.069 --> 00:54:17.849
Umm yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9728-1
00:54:16.828 --> 00:54:17.389
question.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9742-0
00:54:17.859 --> 00:54:20.801
Maybe that argues for observing
Ridgecrest for another 20 years

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9742-1
00:54:20.801 --> 00:54:21.399
or something.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9741-0
00:54:21.299 --> 00:54:21.519
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9744-0
00:54:22.399 --> 00:54:22.689
Listen.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9749-0
00:54:23.269 --> 00:54:24.149
OK, thanks.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9750-0
00:54:25.079 --> 00:54:25.829
Thanks for your question.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9763-0
00:54:33.019 --> 00:54:36.209
Got a question from Eric
Burdette.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9776-0
00:54:36.219 --> 00:54:38.169
Eric, do you wanna unmute
yourself and ask your question?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9780-0
00:54:39.519 --> 00:54:39.719
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9779-0
00:54:40.179 --> 00:54:40.469
And.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9784-0
00:54:41.459 --> 00:54:43.149
So I was.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9797-0
00:54:43.159 --> 00:54:46.929
I was just wondering about the
realities.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9843-0
00:54:46.939 --> 00:54:50.885
Rashad A and if you have looked
at, is there some lower

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9843-1
00:54:50.885 --> 00:54:55.042
temperature realities that do
the sorts of things that you

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9843-2
00:54:55.042 --> 00:54:59.128
were saying about getting
stronger, weaker with different

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9843-3
00:54:59.128 --> 00:55:03.074
stresses and strain rates,
particularly low temperature

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9843-4
00:55:03.074 --> 00:55:03.849
plasticity?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9892-0
00:55:03.909 --> 00:55:08.273
It's a pretty awful formulation,
I think, to implement in the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9892-1
00:55:08.273 --> 00:55:12.284
models because the stress is
actually inside the the the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9892-2
00:55:12.284 --> 00:55:16.225
exponential term with the
temperature dependence, so it

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9879-0
00:55:14.529 --> 00:55:14.849
Yeah, yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9892-3
00:55:16.225 --> 00:55:18.829
ends up being kind of a nasty
thing.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9918-0
00:55:18.839 --> 00:55:24.402
But instead of being a linear
linear in log space like power

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9918-1
00:55:24.402 --> 00:55:27.959
laws are, they can to have a
changing.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9971-0
00:55:28.389 --> 00:55:33.446
They have a changing exponent
and if you use a, if you use the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9927-0
00:55:30.219 --> 00:55:30.349
But.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9971-1
00:55:33.446 --> 00:55:38.020
realities with a stress squared
term out in front of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9971-2
00:55:38.020 --> 00:55:43.318
exponential term, they go to n =
2 at low stresses and low strain

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9969-0
00:55:42.189 --> 00:55:42.409
Right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9971-3
00:55:43.318 --> 00:55:43.799
rates.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9996-0
00:55:43.809 --> 00:55:47.305
And as as you go towards
transient high stresses, they'll

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/9996-1
00:55:47.305 --> 00:55:50.619
go to these higher order much
higher order power laws.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-0
00:55:50.629 --> 00:55:54.552
So you and I think typically the
the stresses and strain rates

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-1
00:55:54.552 --> 00:55:58.225
kind of end up often end up
somewhere near this transition

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-2
00:55:58.225 --> 00:56:02.210
zone that could make the Realogy
look like, you know, if you're

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10030-0
00:55:58.619 --> 00:55:58.849
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-3
00:56:02.210 --> 00:56:05.946
mixing, if you're kind of in
between the fusion dislocation

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-4
00:56:05.946 --> 00:56:09.619
sleep and low temperature
plasticity, you end up with some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10058-0
00:56:07.349 --> 00:56:07.499
But.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-5
00:56:09.619 --> 00:56:13.231
composite composite reality
that's sort of between any of

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10075-0
00:56:12.049 --> 00:56:12.349
Right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-6
00:56:13.231 --> 00:56:17.091
the any of them that just makes
you go what the heck is going

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10085-0
00:56:16.289 --> 00:56:16.819
Right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10113-0
00:56:16.929 --> 00:56:22.153
I I I think yeah, it reminds me
a lot of I think some of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10095-7
00:56:17.091 --> 00:56:17.589
on? Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10098-0
00:56:17.769 --> 00:56:17.979
No.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10113-1
00:56:22.153 --> 00:56:25.749
work of Lars Hanson and and
coauthors uh.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10116-0
00:56:26.379 --> 00:56:27.009
And so we have.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10122-0
00:56:27.089 --> 00:56:28.889
We were thinking a lot about.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10142-0
00:56:30.319 --> 00:56:35.515
Those sort of that, that kind of
formulation for transients or

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10142-1
00:56:35.515 --> 00:56:38.649
you know, the power law burgers
type.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10170-0
00:56:40.239 --> 00:56:45.688
Which which I know there are
some people who really like and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10181-0
00:56:45.399 --> 00:56:48.279
Yeah, it depends on what camp
you're in, right?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10170-1
00:56:45.688 --> 00:56:46.939
I'm not, I am.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10203-0
00:56:48.839 --> 00:56:53.218
Yeah, it it seems like it's it's
a little more of a of a belief

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10203-1
00:56:53.218 --> 00:56:57.529
system thing and we didn't like,
I don't do those experiments.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10215-0
00:56:57.539 --> 00:57:02.419
So I didn't wanna pick a side
but but.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10246-0
00:57:02.429 --> 00:57:05.256
But you're right, like you can
do that, but then there are

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10246-1
00:57:05.256 --> 00:57:08.274
simpler ways to get transient
strengthening just by saying you

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10246-2
00:57:08.274 --> 00:57:09.519
have grain size evolution.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10250-0
00:57:09.609 --> 00:57:11.339
For example, you have.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10249-0
00:57:09.719 --> 00:57:10.299
Yeah, yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10280-0
00:57:13.229 --> 00:57:18.292
That they're just like maybe
there is something to do with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10280-1
00:57:18.292 --> 00:57:23.183
the the coupling between
temperature evolution back with

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10280-2
00:57:23.183 --> 00:57:25.929
the back with strain and stress.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10333-0
00:57:26.079 --> 00:57:30.212
So there are different ways,
which is why I didn't get into a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10300-0
00:57:28.949 --> 00:57:29.149
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10333-1
00:57:30.212 --> 00:57:34.277
specific form, but I'm just
pointing out that there is maybe

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10333-2
00:57:34.277 --> 00:57:38.143
a need to invoke a transient
realogy because uh, I should

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10333-3
00:57:38.143 --> 00:57:40.809
make my motivation is a little
clearer.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10332-0
00:57:39.959 --> 00:57:40.229
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10363-0
00:57:41.709 --> 00:57:45.789
There have been papers in the
last about maybe a decade or a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10363-1
00:57:45.789 --> 00:57:50.135
little more, saying that steady
state flow laws are insufficient

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10363-2
00:57:50.135 --> 00:57:52.409
to explain geodetic
observations.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-0
00:57:52.819 --> 00:57:57.071
And I think those kinds of
inferences come about from a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-1
00:57:57.071 --> 00:58:01.627
place where you have already
assumed very strongly what the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-2
00:58:01.627 --> 00:58:05.879
grain size is, what the thermal
structure is and and in

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10404-0
00:58:04.889 --> 00:58:05.549
Yeah, yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-3
00:58:05.879 --> 00:58:10.435
contrast, if you just look at
the late intersec strain rate

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-4
00:58:10.435 --> 00:58:14.687
and tie it back to what the
reality that you would have

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-5
00:58:14.687 --> 00:58:18.712
calibrated from the post session
period, there is an

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-6
00:58:18.712 --> 00:58:23.647
inconsistency there because the
post seismic viscosity is the OR

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10462-7
00:58:23.647 --> 00:58:27.899
the the power law profiles that
you infer are too weak.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10475-0
00:58:28.969 --> 00:58:31.319
To have the same localization
later on.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10535-0
00:58:31.589 --> 00:58:36.218
So our motivation is to point
out that there there is a need

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10535-1
00:58:36.218 --> 00:58:40.999
for a transient realogy without
picking which Realogy it is as

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10535-2
00:58:40.999 --> 00:58:45.856
opposed to saying that you know
with the choice of grain sizes,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10511-0
00:58:42.959 --> 00:58:43.119
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10535-3
00:58:45.856 --> 00:58:47.829
joints of thermal profile.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10525-0
00:58:47.439 --> 00:58:47.919
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10531-0
00:58:47.999 --> 00:58:48.509
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10545-0
00:58:48.699 --> 00:58:52.110
You don't wanna pick something
specific because then you get

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10545-1
00:58:52.110 --> 00:58:52.669
into it's.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10590-0
00:58:52.719 --> 00:58:56.187
It's really specific to whatever
you're looking at, and it does

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10590-1
00:58:56.187 --> 00:58:59.654
it hold and you know all that I
I was really curious about, you

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10578-0
00:58:57.559 --> 00:58:58.029
Exactly.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10590-2
00:58:59.654 --> 00:59:03.230
know, you show you put up a plot
of N and and and pre exponential

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10590-3
00:59:03.230 --> 00:59:03.609
factor.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10616-0
00:59:03.799 --> 00:59:08.975
So where do the hearts and pulse
stead and send a fall on that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10616-1
00:59:08.975 --> 00:59:11.439
plot there are there are they?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10621-0
00:59:10.059 --> 00:59:10.739
Ohh it's.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10629-0
00:59:14.429 --> 00:59:14.759
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10633-0
00:59:14.819 --> 00:59:15.359
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10643-0
00:59:14.849 --> 00:59:15.039
And.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10636-0
00:59:15.429 --> 00:59:15.679
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10652-0
00:59:15.689 --> 00:59:19.129
For for 3.5, it's like it's bang
in there.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10654-0
00:59:20.539 --> 00:59:21.789
OK, interesting.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10676-0
00:59:21.919 --> 00:59:24.142
Well, that's, I mean that's
that's a good, that's a good

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10670-0
00:59:22.009 --> 00:59:22.589
OK.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10676-1
00:59:24.142 --> 00:59:24.649
sanity check.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10684-0
00:59:25.069 --> 00:59:28.689
So, but it's N of 3.5 for.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10697-0
00:59:31.239 --> 00:59:36.169
Not for, not for, not for uh
olivine.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10716-0
00:59:36.259 --> 00:59:42.119
It's for N 3.5 for quartz, so
it's a really weak Realogy.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10728-0
00:59:42.649 --> 00:59:46.249
It it's somewhere between quartz
and wet olivine.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10725-0
00:59:46.979 --> 00:59:47.489
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10730-0
00:59:47.789 --> 00:59:48.009
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10765-0
00:59:48.019 --> 00:59:51.074
Which is probably, you know,
it's probably we don't know,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10765-1
00:59:51.074 --> 00:59:54.286
it's it's probably not just a
giant layer of pure cords or a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10765-2
00:59:54.286 --> 00:59:56.129
giant layer of pure all the
veins.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10763-0
00:59:55.319 --> 00:59:55.499
But.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10771-0
00:59:56.139 --> 00:59:58.429
So there's there's other stuff.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10805-0
00:59:58.439 --> 01:00:02.712
There's other theological stuff
that could be like dissolution,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10805-1
01:00:02.712 --> 01:00:06.985
precipitation, kind of things or
phase boundary mixing or other

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10805-2
01:00:06.985 --> 01:00:10.189
other all sorts of stuff that
can mess that up.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10844-0
01:00:10.199 --> 01:00:13.655
If you really, if you really
wanna get picky about it so that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10844-1
01:00:13.655 --> 01:00:16.943
it's it's good that it's like
in, in in a reasonable range

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10844-2
01:00:16.943 --> 01:00:18.949
though, that's what I want to
know.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10882-0
01:00:18.239 --> 01:00:23.677
But yeah, I mean so the the way
we think about those parameters

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10882-1
01:00:23.677 --> 01:00:28.606
that come out is like if you
have earthquake cycle stress

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10882-2
01:00:28.606 --> 01:00:32.599
changes on the order of 10
megapascal at most.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10895-0
01:00:32.929 --> 01:00:37.149
And more realistically, it's
less than a megapascal, right?

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10915-0
01:00:37.869 --> 01:00:41.352
And you want to elicit some sort
of reasonable response that is

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10901-0
01:00:37.919 --> 01:00:38.099
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10915-1
01:00:41.352 --> 01:00:43.039
then measurable at the surface.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10933-0
01:00:44.069 --> 01:00:48.429
You need to have this parameter
somewhere between quartzite and

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10933-1
01:00:48.429 --> 01:00:49.519
and wet olivine.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10955-0
01:00:49.929 --> 01:00:53.135
Any stiffer than that and your
time series will just be a

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10942-0
01:00:50.079 --> 01:00:50.349
Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10955-1
01:00:53.135 --> 01:00:53.909
straight line.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10965-0
01:00:54.109 --> 01:00:55.429
There will be no curvature to
it.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10962-0
01:00:54.359 --> 01:00:54.749
Yeah.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10971-0
01:00:54.819 --> 01:00:56.619
Yeah, yeah. Umm.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10996-0
01:00:56.339 --> 01:01:00.110
So so those parameters I think
are like just with back of the

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/10996-1
01:01:00.110 --> 01:01:03.699
envelope calculations, they're
kind of reasonable I think.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11053-0
01:01:04.499 --> 01:01:08.910
Yeah, I mean the, the, the, the
review, the hurting costed ones

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11053-1
01:01:08.910 --> 01:01:13.184
are are are experimentally based
that they did, they did some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11053-2
01:01:13.184 --> 01:01:17.595
small adjustments based on some
natural share zone observations

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11038-0
01:01:17.249 --> 01:01:17.539
Alright.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11053-3
01:01:17.595 --> 01:01:21.730
and the a lot of the courts
follow laws are kind of in some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11053-4
01:01:21.730 --> 01:01:23.729
sense pinned in that way too.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11079-0
01:01:24.039 --> 01:01:27.188
That makes a lot of sense that
they would be that they would,

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11075-0
01:01:26.649 --> 01:01:26.949
OK.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11079-1
01:01:27.188 --> 01:01:29.169
they would make sense in that
context.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11083-0
01:01:29.809 --> 01:01:30.499
OK, right.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11087-0
01:01:31.439 --> 01:01:33.549
So anyway, thank thanks a lot.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11097-0
01:01:33.559 --> 01:01:34.359
It was a really good talk.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11098-0
01:01:34.729 --> 01:01:35.569
Thanks for your questions.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11117-0
01:02:04.229 --> 01:02:04.719
You're muted.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11124-0
01:02:06.139 --> 01:02:07.179
We am, am I muted.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11119-0
01:02:07.049 --> 01:02:07.199
No.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11129-0
01:02:08.189 --> 01:02:09.129
Nope, that's me.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11131-0
01:02:08.719 --> 01:02:09.979
Ah, OK, OK.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11134-0
01:02:10.269 --> 01:02:13.099
Umm, my apologies everybody.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11148-0
01:02:14.269 --> 01:02:20.469
I was just saying we'll finish
the official section of the.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11155-0
01:02:22.409 --> 01:02:24.269
Talk for now.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11162-0
01:02:24.999 --> 01:02:26.839
So let's thank our speaker one
more time.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11199-0
01:02:30.199 --> 01:02:34.238
And Rishav has agreed to hang
out in the chat and have some

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11199-1
01:02:34.238 --> 01:02:38.479
additional informal discussions
for the next 20 minutes or so.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11217-0
01:02:38.619 --> 01:02:42.586
If you have additional questions
or would like to chime into that

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11217-1
01:02:42.586 --> 01:02:44.089
discussion, stick around.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11227-0
01:02:44.139 --> 01:02:46.029
But for now, we'll end the
formal section.

0a9ee98d-3fa7-426a-befb-6ac8a3cba553/11231-0
01:02:46.039 --> 01:02:48.309
So thanks everybody.